Two-dimensional Ising strips subject to identical surface fields $h_1{=h}_2>~0$ are studied for temperatures above and below the bulk critical temperature $T_c$ and a range of bulk fields h by means of the density-matrix renormalization-group method. In the case of nonvanishing surface fields, the near-critical behavior of the solvation force $f_{\mathrm{solv}},$ total adsorption $\Gamma ,$ inverse longitudinal correlation length ${\xi }_{\Vert }^{-1}$ and specific heat $C_H$ is strongly influenced by the (pseudo) capillary condensation that occurs below $T_c.$ We obtain scaling functions of $f_{\mathrm{solv}},$ $\Gamma ,$ and ${\xi }_{\Vert }^{-1}.$ $C_H$ exhibits a weakly rounded singularity on crossing the pseudocoexistence line. We contrast these results with those for the case of free boundaries where, for temperatures slightly below $T_c,$ $f_{\mathrm{solv}}$ and $C_H$ exhibit a sharp extremum away from $h=0.\mathrm{}$ Our results have direct repercussions for the properties of near-critical Ising films in three dimensions and we argue that the long-ranged solvation (Casimir) force in confined fluids should be more attractive in the neighborhood of the capillary critical point than exactly at the bulk critical point.

• Received 5 July 2001

DOI:https://doi.org/10.1103/PhysRevE.64.056137